Was the name Nowicki given to jewish people?
You're making an assumption that your Jewish male line ancestor was named Nowicki. That may not be the case. It cannot be ruled out, for example, that your great-great-great-etc-grandmother had an affair and an illegitimate child, probably without the knowledge of her husband, a Pole named Nowicki. Or that they adopted a child, or took in a foundling. Or any of many scenarios where there was no link between genes and surname.
Only research can give an answer, as far as research is capable. Often, research is impossible and the answers you are looking for are irretrievably lost forever as no records exist.
Genes are not tied to surnames, or ethnicity, for that matter, as neatly as you seem to assume. Also, a Jew or Jewish convert could theoretically assume any Polish name for a variety of reasons.